Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
int main() {
  long int a[100000];
  long int k;
  int i, p, n, m;
  a[0] = 1;
  p = 2;
  i = 0;
  scanf("%d", &k);
  while (a[i] < k) {
    i++;
    a[i] = a[i - 1] + p;
    p++;
  }
  n = i;
  int l = 0;
  for (i = 0; i <= n; i++) {
    for (int j = i; j <= n; j++) {
      if (a[i] + a[j] == k) {
        l = 1;
        break;
      }
    }
    if (l == 1) break;
  }
  if (l == 0)
    printf("NO");
  else
    printf("YES");
  return 0;
}